A machine costing $$3,000$ must be replaced at the end of $8$ years. The resale value of the machine at the time of replacement is $$600.$ At what annual discount rate $($compounded annually$)$ would it be equally economical to use a similar machine costing $$4,000$ with a life of $8$ years and a resale value of $$1,900?($Assume no taxes.$)$ a$.2\mathrm{.}4\%$ b$.2\mathrm{.}7\%$ c$.3\mathrm{.}0\%$ d$.3\mathrm{.}3\%$ e$.3\mathrm{.}6\%$